Adjoint bi-continuous semigroups and semigroups on the space of measures

For a given bi-continuous semigroup T on a Banach space X we define its adjoint on an appropriate closed subspace X^o of the norm dual X'. Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology (X^o,X). An application is the following: For K a Polish space we consider operator semigroups on the space C(K) of bounded, continuous functions (endowed with the compact-open topology) and on the space M(K) of bounded Baire measures (endowed with the weak*-topology). We show that bi-continuous semigroups on M(K) are precisely those that are adjoints of a bi-continuous semigroups on C(K). We also prove that the class of bi-continuous semigroups on C(K) with respect to the compact-open topology coincides with the class of equicontinuous semigroups with respect to the strict topology. In general, if K is not Polish space this is not the case

Error estimates for the discretization of the velocity tracking problem

In this paper we are continuing our work (Casas and Chrysafinos, SIAM J Numer Anal 50(5):2281–2306, 2012), concerning a priori error estimates for the velocity tracking of two-dimensional evolutionary Navier–Stokes flows. The controls are of distributed type, and subject to point-wise control constraints. The discretization scheme of the state and adjoint equations is based on a discontinuous time-stepping scheme (in time) combined with conforming finite elements (in space) for the velocity and pressure. Provided that the time and space discretization parameters, t and h respectively, satisfy t = Ch2, error estimates of order O(h2) and O(h 3/2 – 2/p ) with p > 3 depending on the regularity of the target and the initial velocity, are proved for the difference between the locally optimal controls and their discrete approximations, when the controls are discretized by the variational discretization approach and by using piecewise-linear functions in space respectively. Both results are based on new duality arguments for the evolutionary Navier–Stokes equations

Factors influencing stream baseflow transit times in tropical montane watersheds

Stream water mean transit time (MTT) is a fundamental hydrologic parameter that integrates the distribution of sources, flow paths, and storages present in catchments. However, in the tropics little MTT work has been carried out, despite its usefulness for providing important information on watershed functioning at different spatial scales in (largely) ungauged basins. In particular, very few studies have quantified stream MTTs or have related these to catchment characteristics in tropical montane regions. Here we examined topographic, land use/cover and soil hydraulic controls on baseflow transit times for nested catchments (0.1–34 km2) within a humid mountainous region, underlain by volcanic soil (Andisols) in central Veracruz (eastern Mexico). We used a 2-year record of bi-weekly isotopic composition of precipitation and stream baseflow data to estimate MTT. Land use/cover and topographic parameters (catchment area and form, drainage density, slope gradient and length) were derived from geographic information system (GIS) analysis. Soil water retention characteristics, and depth and permeability of the soil–bedrock interface were obtained from intensive field measurements and laboratory analysis. Results showed that baseflow MTTs ranged between 1.2 and 2.7 years across the 12 study catchments. Overall, MTTs across scales were mainly controlled by catchment slope and the permeability observed at the soil–bedrock interface. In association with topography, catchment form and the depth to the soil–bedrock interface were also identified as important features influencing baseflow MTTs. The greatest differences in MTTs were found both within groups of small (0.1–1.5 km2) and large (14–34 km2) catchments. Interestingly, the longest stream MTTs were found in the headwater cloud forest catchments

Ecohydrological advances and applications in plant-water relations research: a review

Aims The field of ecohydrology is providing new theoretical frameworks and methodological approaches for understanding the complex interactions and feedbacks between vegetation and hydrologic flows at multiple scales. Here we review some of the major scientific and technological advances in ecohydrology as related to understanding the mechanisms by which plant–water relations influence water fluxes at ecosystem, watershed and landscape scales. Important Findings We identify several cross-cutting themes related to the role of plant– water relations in the ecohydrological literature, including the contrasting dynamics of water-limited and water-abundant ecosystems, transferring information about water fluxes across scales, understanding spatiotemporal heterogeneity and complexity, ecohydrological triggers associated with threshold behavior and shifts between alternative stable states and the need for long-term data sets at multiple scales. We then show how these themes are embedded within three key research areas where improved understanding of the linkages between plant–water relations and the hydrologic cycle have led to important advances in the field of ecohydrology: upscaling water fluxes from the leaf to the watershed and landscape, effects of plant–soil interactions on soil moisture dynamics and controls exerted by plant water use patterns and mechanisms on streamflow regime. In particular, we highlight several pressing environmental challenges facing society today where ecohydrology can contribute to the scientific knowledge for developing sound management and policy solutions.We conclude by identifying key challenges and opportunities for advancing contributions of plant–water relations research to ecohydrology in the future